Paul-Hermann Balduf
Topological quantum field theory and the odd graph complex
Recent articles by Davide Gaiotto and collaborators resulted in a new setup for parametric Feynman integrals in topological quantum field theories. In 2408.03192, joint with Davide Gaiotto, we developed a description of these integrands in terms of standard graph polynomials, and used it to give a new proof for the Kontsevich formality theorem.
My talk will focus on the recent result 2503.09558, together with Simone Hu, that this "topological" integral coincides with an integral that had been used in cohomology computations of the odd graph complex and of $GL_n$ by Francis Brown and collaborators. This relation implies a very elegant description of the topological integrand in terms of the Pfaffian of a Laplacian matrix, and yet another proof of the Kontsevich formality theorem.
